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# The sequence S is defined by Sn = Sn – 1 + Sn – 2 – 1 for each integer

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Math Expert
Joined: 02 Sep 2009
Posts: 47977
The sequence S is defined by Sn = Sn – 1 + Sn – 2 – 1 for each integer  [#permalink]

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27 Jul 2018, 01:23
00:00

Difficulty:

35% (medium)

Question Stats:

75% (02:13) correct 25% (03:09) wrong based on 15 sessions

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The sequence S is defined by $$S_n = S_{n - 1} + S{n - 2} - 1$$ for each integer n ≥ 3. If $$S_1 = 11$$ and $$S_3 = 10$$, what is the value of $$S_5$$?

(A) 0
(B) 9
(C) 10
(D) 18
(E) 19

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Re: The sequence S is defined by Sn = Sn – 1 + Sn – 2 – 1 for each integer  [#permalink]

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27 Jul 2018, 02:00
Sn = Sn−1 + Sn−2 − 1
S1=11 and S3=10, S5 = ?

S3 = S2 + S1 − 1
10 = S2 + 11 - 1
S2 = 0

S4 = S3 + S2 − 1
S4 = 10 + 0 - 1 = 9

S5 = S4 + S3 − 1
S5 = 9 + 11 - 1 = 19

Hence, E.
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Re: The sequence S is defined by Sn = Sn – 1 + Sn – 2 – 1 for each integer &nbs [#permalink] 27 Jul 2018, 02:00
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